Compounded continuously, your investment will grow according to:
Compounded annually, your investment will grow according to:,
where t is measured in years. The former is really just , which is in the same form as the latter but with in place of . So the equivalent rate if compounded annually is , which comes out to something like 6.185%.

I think you get the same thing if you solve the equation you wrote down. You don't need to take logs to solve it, however: